Part 1: The maximum velocity of the Magnum XL-200 roller coaster depends on the

Question

Part 1:

The maximum velocity of the Magnum XL-200 roller coaster depends on the vertical drop from the top of the highest hill to the bottom of that hill. The formula v= 8and square root of h gives the relationship between maximum velocity, v (in feet per second), and height, h (in feet).

What is the domain of the equation? Write your answer in interval notation. Explain why you excluded certain values from the domain both mathematically AND in the context of the question.

Part 2: What is the maximum velocity of the Magnum XL-200 roller coaster in Sandusky, Ohio, when height is approximately 203 feet? Show all work using the equation editor and label your final solution. Round your final answer to the nearest hundredth, but remember you should NOT round in the middle of the question. Write a sentence explaining your answer.

Part 3:What is the height of the coaster when the velocity is 90 ft/sec? Show all work using the equation editor and label your final solution. Round your final answer to the nearest hundredth, but remember you should NOT round in the middle of the question. Write a sentence explaining your answer.

Explanation / Answer

a)

203=(64h)^(1/2)

12996=64h

h=0.222ft

Given:
V=90 ft/s
v=10 ft/s

Unknown:
Height (h)

Formula:
V=squareroot(v + 64h)

(here you start doing work; start by inserting the given)

90 = squareroot(10 + 64h)

start working it with algebra

(square both sides)
8100 = 10 + 64h

subtract 10 ft/s from both sides
8090 = 64h

From here, divide both sides by 64
h = 126.40625

Once you round, you have your answer.
h = 126.4

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